Geometrical Axiomatization for Model Complete Theories of Differential Topological Fields
Geometrical Axiomatization for Model Complete Theories of Differential Topological Fields
复制标题
微分拓扑场模型完备理论的几何公理化
DOI：
10.1305/ndjfl/1163775440
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Cédric Rivière
中科院分区：
文献类型：
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作者：
Nicolas Guzy;Cédric Rivière
本文给出了一个微分提升原理，它提供了一个一般的方法，几何公理化的模型伴侣（如果它存在）的一些理论的微分拓扑场。我们在这里考虑的拓扑场实际上是[vdD1，2.11]意义下的拓扑系统，我们发展的提升原理是D. Pierce和A. Pillay in [PP].此外，它提供了一个几何的替代公理化[Tr]和[GP]，其中作者还建立了一些模型完备理论的微分场的公理的一般计划。我们首先描述了存在封闭模型的一个给定的理论微分拓扑领域，然后，在一个额外的假设下的largeness，我们展示了如何修改这种表征得到一个一般计划的一阶公理的模型伴侣的任何大型理论微分拓扑领域。我们的结论与应用程序的提升原理证明，在存在封闭模型的一个大理论的微分拓扑领域，喷气空间是稠密的周围的拓扑空间。1基本代数几何在下文中K是特征为零的域，Ω是K的充分饱和初等扩张（特别是Ω在K上具有无限超越度），Ω表示Ω的代数闭包。第一作者由FNRS资助。第二位提交人得到了弗里亚的资助。
In this paper we give a differential lifting principle which provides a general method to geometrically axiomatize the model companion (if it exists) of some theories of differential topological fields. The topological fields we consider here are in fact topological systems in the sense of [vdD1, 2.11], and the lifting principle we develop is a generalization of the geometric axiomatization of the theory DCF0 given by D. Pierce and A. Pillay in [PP]. Moreover it provides a geometric alternative to the axiomatizations obtained in [Tr] and [GP] where the authors also build general schemes of axioms for some model complete theories of differential fields. We first characterize the existentially closed models of a given theory of differential topological fields and then, under an additional hypothesis of largeness, we show how to modify this characterization to get a general scheme of first-order axioms for the model companion of any large theory of differential topological fields. We conclude with an application of this lifting principle proving that in existentially closed models of a large theory of differential topological fields, the jet-spaces are dense in their ambient topological space. 1 Basic algebraic geometry In what follows K is a field of characteristic zero, Ω is a sufficiently saturated elementary extension of K (in particular Ω is of infinite transcendence degree over K) and Ω denotes the algebraic closure of Ω. ∗The first author is supported by a FNRS grant. The second author is supported by a FRIA grant.